Finite Group Databasebeta

← #36524937

Subgroups — #36524937

Order 22784.

590 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26030264C211yesmaximal, characteristic
2#26029401C211yesmaximal, characteristic, complemented
3#26029370C211yesmaximal, characteristic, complemented
4#26019163C211yesmaximal, characteristic, complemented
5#26019158C211yesmaximal, characteristic, complemented
6#26019145C211yesmaximal, characteristic, complemented
7#26019139C211yesmaximal, characteristic, complemented
8#26019120C211yesmaximal, characteristic, complemented
9#26019113C211yesmaximal, characteristic, complemented
10#26019092C211yesmaximal, characteristic, complemented
11#26019085C211yesmaximal, characteristic, complemented
12#26019022C211yesmaximal, characteristic, complemented
13#26018692C211yesmaximal, characteristic, complemented
14#26018549C211yesmaximal, characteristic, complemented
15C89×#1483C211yesmaximal, characteristic, complemented
16C4×#13083574C2211yescharacteristic
17#19151936C411yescharacteristic
18#19151919C411yescharacteristic
19#19151902C411yescharacteristic
20#19151895C411yescharacteristic
21#19151817C411yescharacteristic
22#19151810C411yescharacteristic
23#19151758C411yescharacteristic
24#19151741C411yescharacteristic
25#19151729C2211yescharacteristic
26#19151725C2211yescharacteristic
27#19151725C2211yescharacteristic
28Q8×#10623494C2211yescharacteristic
29C4×#13083564C2211yescharacteristic
30C4×#13083561C2211yescharacteristic
31C4×#13083562C2211yescharacteristic
32C4×#13083559C2211yescharacteristic
33#19151676—21no—
34#19151676C2211yescharacteristic
35#19151675C2211yescharacteristic
36#19151675C2211yescharacteristic
37#19151670—21no—
38#19151669—21no—
39#19151669—21no—
40D4×#10623494C2211yescharacteristic
41#19151659—21no—
42#19151654—21no—
43#19151651C2211yescharacteristic
44#19151651C2211yescharacteristic
45#19151625—21no—
46#19151622C2211yescharacteristic
47#19151620—21no—
48#19151348C2211yescharacteristic
49#19151348C2211yescharacteristic
50#19151348C2211yescharacteristic
51#19151348C2211yescharacteristic
52#19151330C2211yescharacteristic
53#19151330C2211yescharacteristic
54#19151327C2211yescharacteristic
55#19151327C2211yescharacteristic
56#19151320C2211yescharacteristic
57#19151320C2211yescharacteristic
58#19151319C2211yescharacteristic
59C8×#10623494C2211yescharacteristic
60#529×C89C2211yescharacteristic
61C2×C4⋊C8×C89C2211yescharacteristic
62C4×M16×C89C2211yescharacteristic
63Q8⋊C8×C89C2211yescharacteristic
64Q8⋊C8×C89C2211yescharacteristic
65D4⋊C8×C89C2211yescharacteristic
66D4⋊C8×C89C2211yescharacteristic
67C2×#13083574C2×C411yescharacteristic
68C2×#13083564C2×C411yescharacteristic
69C2×#13083562C2×C411yescharacteristic
70C2×#13083561C2×C411yescharacteristic
71C2×#13083559C2×C411yescharacteristic
72C2×#13083558—21no—
73C2×#13083558—21no—
74C2×#13083557—21no—
75C2×#13083557—21no—
76C22×#10623494—21no—
77C4×Dic178C2×C411yescharacteristic
78C4×Dic178C2311yescharacteristic
79C4×D356C2×C411yescharacteristic
80C4×D356C2311yescharacteristic
81C4×C22⋊D89—21no—
82C4×C22⋊D89—21no—
83#15667971C2×C411yescharacteristic
84#15667969—21no—
85C42×D89—21no—
86#15667945C2×C411yescharacteristic
87#15667945C2×C411yescharacteristic
88#15667943C2×C411yescharacteristic
89#15667943C2×C411yescharacteristic
90C4⋊#10623494—21no—
91C4⋊#10623494—21no—
92C4⋊#10623494—21no—
93C4⋊#10623494C2×C411yescharacteristic
94C4⋊#10623494C2×C411yescharacteristic
95C4⋊#10623494D411yescharacteristic
96C4⋊#10623494D411yescharacteristic
97C4⋊#10623494C2311yescharacteristic
98C4⋊#10623494C2311yescharacteristic
99#15667941—21no—
100#15667941—21no—
101#15667936C2×C411yescharacteristic
102#15667936C2×C411yescharacteristic
103#15667935C2×C411yescharacteristic
104#15667935C2×C411yescharacteristic
105#15667933C2×C411yescharacteristic
106#15667933C2×C411yescharacteristic
107#15667932C2×C411yescharacteristic
108#15667932C2×C411yescharacteristic
109C22⋊#10623494—21no—
110C22⋊#10623494—21no—
111C22⋊#10623494C2×C411yescharacteristic
112C22⋊#10623494C2×C411yescharacteristic
113C22⋊#10623494D411yescharacteristic
114C22⋊#10623494D411yescharacteristic
115#15667924—21no—
116#15667924—21no—
117#15667923—21no—
118#15667922—21no—
119#15667922—21no—
120C4×#10623494—21no—
121C4×#10623494C2311yescharacteristic
122C4×#10623494C2311yescharacteristic
123C4×#10623494C2311yescharacteristic
124C4×#10623494C2311yescharacteristic
125C2×M16×C89—21no—
126C22×C8×C89—21no—
127#126×C89—21no—
128#125×C89C2×C411yescharacteristic
129#124×C89C2×C411yescharacteristic
130#123×C89—21no—
131C22⋊Q8×C89C2×C411yescharacteristic
132#121×C89C2×C411yescharacteristic
133C4×Q8×C89C2311yescharacteristic
134C4×D4×C89—21no—
135C4×D4×C89C2311yescharacteristic
136#117×C89—21no—
137C2×C42×C89C2311yescharacteristic
138C4⋊C8×C89—21no—
139C4⋊C8×C89C2311yescharacteristic
140C4⋊C8×C89C2311yescharacteristic
141#97×C89—21no—
142C4×C8×C89C2311yescharacteristic
143C4×C8×C89C2311yescharacteristic
144#13083574—41no—
145#13083574—41no—
146C2×Dic178C22×C411yescharacteristic
147C2×D356C22×C411yescharacteristic
148C2×C22⋊D89—21no—
149C2×C4×D89—21no—
150C2×C4×D89—21no—
151C2×C4×D89—21no—
152#13083564—41no—
153#13083562—41no—
154#13083561—41no—
155#13083559—41no—
156#13083558—81no—
157#13083558—81no—
158#13083557—81no—
159#13083557—81no—
160C2×#10623494—21no—
161C2×#10623494—21no—
162C2×#10623494—81no—
163C2×#10623494C22×C411yescharacteristic
164C2×#10623494C22×C411yescharacteristic
165C2×#10623494C22×C411yescharacteristic
166C2×#10623494C22×C411yescharacteristic
167C2×#10623494C2×D411yescharacteristic
168C2×#10623494C2×D411yescharacteristic
169C2×#10623494C2×D411yescharacteristic
170C2×#10623494C2×D411yescharacteristic
171C4⋊Dic89C22×C411yescharacteristic
172C4⋊Dic89C22×C411yescharacteristic
173#13083553—21no—
174#13083553—21no—
175C22⋊Dic89—21no—
176#13083551—21no—
177#13083551—21no—
178C4×Dic89—21no—
179C4×Dic89—21no—
180C4×Dic89—21no—
181C2×Q8×C89C22×C411yescharacteristic
182C2×D4×C89—21no—
183C2×D4×C89C22×C411yescharacteristic
184C22×C4×C89—21no—
185C22×C4×C89C22×C411yescharacteristic
186C22×C4×C89C2×D411yescharacteristic
187C22×C4×C89#4111yescharacteristic
188M16×C89—42no—
189C2×C8×C89—21no—
190C2×C8×C89—21no—
191C2×C8×C89—21no—
192C2×C8×C89—21no—
193C2×C8×C89—81no—
194C4⋊C4×C89—21no—
195C4⋊C4×C89—21no—
196C4⋊C4×C89—21no—
197C4⋊C4×C89—21no—
198C4⋊C4×C89C22×C411yescharacteristic
199C4⋊C4×C89C22×C411yescharacteristic
200C22⋊C4×C89—21no—
201C22⋊C4×C89—21no—
202C22⋊C4×C89—21no—
203C22⋊C4×C89—21no—
204C22⋊C4×C89—21no—
205C42×C89—21no—
206C42×C89C22×C411yescharacteristic
207C42×C89C2×D411yescharacteristic
208C42×C89#4111yescharacteristic
209C42×C89C2411yescharacteristic
210C23×C89—21no—
211C23×C89C4×D411yescharacteristic
212C22×D89—21no—
213Q8×C89—21no—
214Q8×C89—21no—
215D4×C89—21no—
216D4×C89—21no—
217D4×C89—81no—
218C2×C4×C89—21no—
219C2×C4×C89—21no—
220C2×C4×C89—21no—
221C2×C4×C89—21no—
222C2×C4×C89—21no—
223C2×C4×C89—21no—
224C2×C4×C89—21no—
225C2×C4×C89—41no—
226C2×C4×C89—41no—
227C2×C4×C89—41no—
228C2×C4×C89C4×D411yescharacteristic
229C2×C4×C89C4×D411yescharacteristic
230C2×C4×C89C4×D411yescharacteristic
231C2×C4×C89C23×C411yescharacteristic
232C2×C4×C89C22×D411yescharacteristic
233C2×C4×C89C2×#4111yescharacteristic
234C22⋊D89—42no—
235C2×Dic89—21no—
236C2×Dic89—21no—
237C2×Dic89—21no—
238D356—21no—
239D356—21no—
240C4×D89—42no—
241C4×D89—41no—
242C4×D89—41no—
243C4×D89—81no—
244Dic178—21no—
245Dic178—21no—
246C8×C89—22no—
247C8×C89—41no—
248C8×C89—41no—
249C8×C89—41no—
250#10623494—21no—
251#10623494—21no—
252#10623494—21no—
253#10623494—21no—
254#10623494—21no—
255#10623494—21no—
256#10623494—21no—
257#10623494—21no—
258#10623494—41no—
259#10623494—41no—
260C22×C89—21no—
261C22×C89—21no—
262C22×C89—21no—
263C22×C89—41no—
264C22×C89—41no—
265C22×C89—41no—
266C22×C89C2×C4×D411yescharacteristic
267C2×D89—41no—
268C2×D89—41no—
269C2×D89—41no—
270C4×C89—21no—
271C4×C89—21no—
272C4×C89—21no—
273C4×C89—21no—
274C4×C89—41no—
275C4×C89—41no—
276C4×C89—41no—
277C4×C89#56811yescharacteristic
278C4×C89#56811yescharacteristic
279C4×C89#57711yescharacteristic
280C4×C89#57711yescharacteristic
281Dic89—41no—
282Dic89—41no—
283Dic89—41no—
284#17955—891nomaximal, Sylow
285C2×C89—41no—
286C2×C89—81no—
287C2×C89#293011yescharacteristic
288C2×C89#295211yescharacteristic
289C2×C89#295611yescharacteristic
290D89—81no—
291#3102—891no—
292#2993—891no—
293#2989—891no—
294#1594—891no—
295#1593—891no—
296#1590—891no—
297#1590—891no—
298#1587—891no—
299#1586—891no—
300#1583—891no—
301#1582—891no—
302#1570—891no—
303#1489—891no—
304#1483D8911yescharacteristic, complemented
305#1453—891no—
306C89#1795511yescharacteristic, complemented, Sylow
307#529C2×D8911yescharacteristic
308C4×#41—891no—
309#485—891no—
310#482—891no—
311#479—891no—
312#478—891no—
313#464—891no—
314#463—891no—
315#452—891no—
316#449—891no—
317#446—891no—
318#446—891no—
319#446—891no—
320C8×Q8—891no—
321C4×Q16—891no—
322C4×SD16—891no—
323C4×SD16—891no—
324C4×D8—891no—
325#436—891no—
326#436—891no—
327#436—891no—
328#436—1781no—
329#435—1781no—
330#435—1781no—
331#435—1781no—
332C8×D4—891no—
333#433—1781no—
334#432—1781no—
335#431—891no—
336#431—891no—
337#424—1781no—
338#423—891no—
339#423—1781no—
340C2×C4⋊C8C2×D8911yescharacteristic
341C4×M16C2×D8911yescharacteristic
342#334—891no—
343#334—891no—
344#334—891no—
345#334—891no—
346Q8⋊C8—891no—
347Q8⋊C8—891no—
348Q8⋊C8C2×D8911yescharacteristic
349Q8⋊C8C2×D8911yescharacteristic
350D4⋊C8—891no—
351D4⋊C8—891no—
352D4⋊C8C2×D8911yescharacteristic
353D4⋊C8C2×D8911yescharacteristic
354#322—891no—
355#322—891no—
356#322—891no—
357C82—891no—
358C2×#41—891no—
359C2×Q16—891no—
360C2×SD16—891no—
361C2×SD16—891no—
362C2×D8—891no—
363C2×M16—21no—
364C2×M16—1781no—
365C2×M16—1781no—
366C2×M16—1781no—
367C2×M16—1781no—
368C22×C8—21no—
369C22×C8—1781no—
370#126—21no—
371#125C4×D8911yescharacteristic
372#124C4×D8911yescharacteristic
373#123—21no—
374C22⋊Q8C4×D8911yescharacteristic
375#121C4×D8911yescharacteristic
376C4×Q8—891no—
377C4×Q8—891no—
378C4×Q8C22×D8911yescharacteristic
379C4×D4—21no—
380C4×D4—891no—
381C4×D4—891no—
382C4×D4—1781no—
383C4×D4—1781no—
384C4×D4C22×D8911yescharacteristic
385#117—21no—
386#117—891no—
387#117—1781no—
388C2×C42—1781no—
389C2×C42C22×D8911yescharacteristic
390#107—891no—
391#107—891no—
392#106—891no—
393#106—891no—
394C4⋊C8—21no—
395C4⋊C8—891no—
396C4⋊C8—891no—
397C4⋊C8—891no—
398C4⋊C8—891no—
399C4⋊C8—891no—
400C4⋊C8—891no—
401C4⋊C8—1781no—
402C4⋊C8—1781no—
403C4⋊C8—1781no—
404C4⋊C8—1781no—
405C4⋊C8—1781no—
406C4⋊C8C22×D8911yescharacteristic
407C4⋊C8C22×D8911yescharacteristic
408#103—891no—
409#103—891no—
410#103—891no—
411#103—891no—
412#102—891no—
413#102—891no—
414#102—891no—
415#102—891no—
416C22⋊C8—891no—
417C22⋊C8—891no—
418C22⋊C8—891no—
419C22⋊C8—891no—
420C22⋊C8—1781no—
421C22⋊C8—1781no—
422C22⋊C8—1781no—
423C22⋊C8—1781no—
424#97—21no—
425#97—1781no—
426#97—1781no—
427#97—1781no—
428C4×C8—891no—
429C4×C8—891no—
430C4×C8—891no—
431C4×C8—891no—
432C4×C8—1781no—
433C4×C8C22×D8911yescharacteristic
434C4×C8C22×D8911yescharacteristic
435#41—3561no—
436#41—3561no—
437C2×Q8—891no—
438C2×Q8C2×C4×D8911yescharacteristic
439C2×D4—21no—
440C2×D4—891no—
441C2×D4—1781no—
442C2×D4C2×C4×D8911yescharacteristic
443C22×C4—21no—
444C22×C4—1781no—
445C22×C4—1781no—
446C22×C4—1781no—
447C22×C4C2×C4×D8911yescharacteristic
448C22×C4D4×D8911yescharacteristic
449C22×C4#1308357311yescharacteristic
450Q16—3561no—
451SD16—3561no—
452SD16—3561no—
453D8—3561no—
454M16—42no—
455M16—7121no—
456M16—7121no—
457M16—7121no—
458M16—7121no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—81no—
464C2×C8—891no—
465C2×C8—891no—
466C2×C8—891no—
467C2×C8—891no—
468C2×C8—891no—
469C2×C8—891no—
470C2×C8—891no—
471C2×C8—891no—
472C2×C8—1781no—
473C2×C8—1781no—
474C2×C8—7121no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—891no—
480C4⋊C4—891no—
481C4⋊C4—1781no—
482C4⋊C4—1781no—
483C4⋊C4C2×C4×D8911yescharacteristic
484C4⋊C4C2×C4×D8911yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—1781no—
491C22⋊C4—1781no—
492C22⋊C4—1781no—
493C42—21no—
494C42—1781no—
495C42—1781no—
496C42—1781no—
497C42C2×C4×D8911yescharacteristic
498C42D4×D8911yescharacteristic
499C42#1308357311yescharacteristic
500C42C23×D8911yescharacteristic
501C23—21no—
502C23—1781no—
503C23#1566797211yescharacteristic
504Q8—21no—
505Q8—21no—
506Q8—1781no—
507Q8—1781no—
508D4—21no—
509D4—21no—
510D4—81no—
511D4—3562no—
512D4—1781no—
513D4—1781no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—3562no—
525C2×C4—3561no—
526C2×C4—3561no—
527C2×C4—1781no—
528C2×C4—1781no—
529C2×C4—1781no—
530C2×C4—7121no—
531C2×C4#1566797211yescharacteristic
532C2×C4#1566797211yescharacteristic
533C2×C4#1566797211yescharacteristic
534C2×C4C22×C4×D8911yescharacteristic
535C2×C4C2×D4×D8911yescharacteristic
536C2×C4C2×#1308357311yescharacteristic
537C8—22no—
538C8—41no—
539C8—41no—
540C8—41no—
541C8—3561no—
542C8—3561no—
543C8—1781no—
544C8—1781no—
545C8—1781no—
546C8—1781no—
547C8—1781no—
548C8—1781no—
549C8—1781no—
550C8—1781no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—3561no—
558C22—3561no—
559C22—3561no—
560C22C2×#1566797211yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—3561no—
569C4—3561no—
570C4—3561no—
571C4#1915236311yescharacteristic
572C4#1915236311yescharacteristic
573C4#1915240711yescharacteristic
574C4#1915240811yescharacteristic
575C2—41no—
576C2—81no—
577C2—7121no—
578C2#2602895811yescharacteristic
579C2#2602913111yescharacteristic
580C2#2602915811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D89
commutatorC2×C4×C89C23×C4
FrattiniC42C23×D89
FittingC89×#1483C2
socleC22×C89C2×C4×D4
prime radical#19151741C4
cosocleC42×C89C24
hypercenter#1483D89
hypocenterC89#17955
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1483

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #26029401C2semidirect
3. #26029370C2semidirect
4. #26019163C2semidirect
5. #26019158C2semidirect
6. #26019145C2semidirect
7. #26019139C2semidirect
8. #26019120C2semidirect
9. #26019113C2semidirect
10. #26019092C2semidirect
11. #26019085C2semidirect
12. #26019022C2semidirect
13. #26018692C2semidirect
14. #26018549C2semidirect
15. C89×#1483C2semidirect
304. #1483D89semidirect
306. C89#17955semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
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